Abstract
This paper is dedicated to studying the following Schrödinger–Poisson system
where V,K are positive continuous potentials, f is a continuous function and \({\lambda}\) is a positive parameter. We develop a direct approach to establish the existence of one ground state sign-changing solution \({u_\lambda}\) with precisely two nodal domains, by introducing a weaker condition that there exists \({\theta_0\in (0,1)}\) such that
than the usual increasing condition on \({f(t)/|t|^3}\). Under the above condition, we also prove that the energy of any sign-changing solution is strictly larger than two times the least energy, and give a convergence property of \({u_\lambda}\) as \({\lambda\searrow 0}\).
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This work is partially supported by the National Natural Science Foundation of China (No: 11571370).
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Chen, S., Tang, X. Ground state sign-changing solutions for a class of Schrödinger–Poisson type problems in \({\mathbb{R}^{3}}\) . Z. Angew. Math. Phys. 67, 102 (2016). https://doi.org/10.1007/s00033-016-0695-2
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DOI: https://doi.org/10.1007/s00033-016-0695-2